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Homework Help: Critical points of multivariables

  1. Mar 9, 2009 #1
    1. The problem statement, all variables and given/known data

    Find and classify all critical points of
    [tex]f(x,y) = x^3+2y^3-3x^2-3y^2-12y[/tex]

    2. Relevant equations

    3. The attempt at a solution

    So I've gotten to
    [tex]Fx = 3x^2 - 6x = 0[/tex]
    [tex]Fy = 6y^2 - 6y - 12 = 0[/tex]

    [tex]x=0, x=2, y=-1, y=2[/tex]

    Now I can't remember how to find the critical points from here.
    Any help is appreciated!
  2. jcsd
  3. Mar 9, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    The critical points are where Fx=0 AND Fy=0. Why is that hard to remember? Offhand, I would say you have four of them.
  4. Mar 9, 2009 #3
    Oh yeah, thanks. And it's hard to remember because I'm still a student.
  5. Mar 10, 2009 #4


    Staff: Mentor

    It's not that much different from how it is with functions of one variable. If y = f(x), you look for values for which f'(x) = 0. With functions of two or more variables, you look for points for which all the partial derivatives are zero.
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